You can take a bus from Wagga Wagga to Cowra via Gundagai Coach Stop and Cootamundra Coach Stop in around 5 h 20 min.
How to get from Wagga Wagga to Cowra
From Wagga Wagga train to Cootamundra Coach Stop then bus to Cowra Coach Stop, Macquarie St. 3 h 53 min $51. From Wagga Wagga bus to Gundagai Coach Stop, bus to Cootamundra Coach Stop, then bus to Cowra Coach Stop, Macquarie St. 5 h 20 min $44. From Wagga Wagga drive to Cowra. 2 h 46 min $29.